Small Engines (Lawn Mowers, etc.): B&S repair question

Question
I have an older Yard Man self-propelled walk behind mower with a Briggs engine in very good condition.  The gas tank has cracked, which I will replace.  It is impossible to start.  I was told that instead of trying to rebuild the carb, I should just replace it. Which is the better option?  A new carb will be expensive, so I would be looking at putting about $100 into this mower. I also have seen that there are two carbs available for this model, and I am not sure which to order if I need to.  Model 12v809 Type 1783 Code 01060858

Answer
We rarely replace those carbs. We just clean, install a new inlet needle and seat, and a float bowl gasket.  

If someone brings in just the carburetor we rebuilt for $25.00 plus parts.  It usually runs about $40.00 for the entire job.

Do you have an air compressor?

Let me know.
Eric